Question: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.50$, and bags of cookies cost $$3.00$, and sales equaled $$53.00$ in total. There were $5$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+3y = 53}$ ${y = x+5}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+5}$ for $y$ in the first equation. ${6.5x + 3}{(x+5)}{= 53}$ Simplify and solve for $x$ $ 6.5x+3x + 15 = 53 $ $ 9.5x+15 = 53 $ $ 9.5x = 38 $ $ x = \dfrac{38}{9.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+5}$ to find $y$ ${y = }{(4)}{ + 5}$ ${y = 9}$ You can also plug ${x = 4}$ into $ {6.5x+3y = 53}$ and get the same answer for $y$ ${6.5}{(4)}{ + 3y = 53}$ ${y = 9}$ $4$ bags of candy and $9$ bags of cookies were sold.